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Table of Contents:

• What does the dataset contain?
• EDA
• Training
• • Neural Network
• • Logistic Regression
• • Random Forest
• Further Questions
• • Which features are the most important?

What does the dataset contain?

Features are computed from a digitized image of a fine needle aspirate (FNA) of a breast mass. They describe characteristics of the cell nuclei present in the image.

1. ID number
2. Diagnosis (M = malignant, B = benign)

Ten real-valued features are computed for each cell nucleus:

3. radius (mean of distances from center to points on the perimeter)
4. texture (standard deviation of gray-scale values)
5. perimeter
6. area
7. smoothness (local variation in radius lengths)
8. compactness (perimeter^2 / area - 1.0)
9. concavity (severity of concave portions of the contour)
10. concave points (number of concave portions of the contour)
11. symmetry
12. fractal dimension ("coastline approximation" - 1)

Exploratory Data Analysis

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn import preprocessing

df = pd.read_csv('data.csv')

df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 569 entries, 0 to 568
Data columns (total 33 columns):
 #   Column                   Non-Null Count  Dtype  
---  ------                   --------------  -----  
 0   id                       569 non-null    int64  
 1   diagnosis                569 non-null    object 
 2   radius_mean              569 non-null    float64
 3   texture_mean             569 non-null    float64
 4   perimeter_mean           569 non-null    float64
 5   area_mean                569 non-null    float64
 6   smoothness_mean          569 non-null    float64
 7   compactness_mean         569 non-null    float64
 8   concavity_mean           569 non-null    float64
 9   concave points_mean      569 non-null    float64
 10  symmetry_mean            569 non-null    float64
 11  fractal_dimension_mean   569 non-null    float64
 12  radius_se                569 non-null    float64
 13  texture_se               569 non-null    float64
 14  perimeter_se             569 non-null    float64
 15  area_se                  569 non-null    float64
 16  smoothness_se            569 non-null    float64
 17  compactness_se           569 non-null    float64
 18  concavity_se             569 non-null    float64
 19  concave points_se        569 non-null    float64
 20  symmetry_se              569 non-null    float64
 21  fractal_dimension_se     569 non-null    float64
 22  radius_worst             569 non-null    float64
 23  texture_worst            569 non-null    float64
 24  perimeter_worst          569 non-null    float64
 25  area_worst               569 non-null    float64
 26  smoothness_worst         569 non-null    float64
 27  compactness_worst        569 non-null    float64
 28  concavity_worst          569 non-null    float64
 29  concave points_worst     569 non-null    float64
 30  symmetry_worst           569 non-null    float64
 31  fractal_dimension_worst  569 non-null    float64
 32  Unnamed: 32              0 non-null      float64
dtypes: float64(31), int64(1), object(1)
memory usage: 146.8+ KB

All the relevant features are floats and there is an unnecessary feature called "Unnamed: 32" that seems to appear due to this issue with read_csv(): https://www.kaggle.com/discussions/general/354943

df.drop(['id', 'Unnamed: 32'], axis=1, inplace=True)
df.head()

	diagnosis	radius_mean	texture_mean	perimeter_mean	area_mean	smoothness_mean	compactness_mean	concavity_mean	concave points_mean	symmetry_mean	...	radius_worst	texture_worst	perimeter_worst	area_worst	smoothness_worst	compactness_worst	concavity_worst	concave points_worst	symmetry_worst	fractal_dimension_worst
0	M	17.99	10.38	122.80	1001.0	0.11840	0.27760	0.3001	0.14710	0.2419	...	25.38	17.33	184.60	2019.0	0.1622	0.6656	0.7119	0.2654	0.4601	0.11890
1	M	20.57	17.77	132.90	1326.0	0.08474	0.07864	0.0869	0.07017	0.1812	...	24.99	23.41	158.80	1956.0	0.1238	0.1866	0.2416	0.1860	0.2750	0.08902
2	M	19.69	21.25	130.00	1203.0	0.10960	0.15990	0.1974	0.12790	0.2069	...	23.57	25.53	152.50	1709.0	0.1444	0.4245	0.4504	0.2430	0.3613	0.08758
3	M	11.42	20.38	77.58	386.1	0.14250	0.28390	0.2414	0.10520	0.2597	...	14.91	26.50	98.87	567.7	0.2098	0.8663	0.6869	0.2575	0.6638	0.17300
4	M	20.29	14.34	135.10	1297.0	0.10030	0.13280	0.1980	0.10430	0.1809	...	22.54	16.67	152.20	1575.0	0.1374	0.2050	0.4000	0.1625	0.2364	0.07678

5 rows × 31 columns

We drop the "id" and "Unnamed: 32" columns since thery are irrelevant.

def diagnosis_value(diagnosis):
    return 1 if diagnosis == 'M' else 0

Encode the target feature numerically.

df['diagnosis'] = df['diagnosis'].apply(diagnosis_value)
df.head()

	diagnosis	radius_mean	texture_mean	perimeter_mean	area_mean	smoothness_mean	compactness_mean	concavity_mean	concave points_mean	symmetry_mean	...	radius_worst	texture_worst	perimeter_worst	area_worst	smoothness_worst	compactness_worst	concavity_worst	concave points_worst	symmetry_worst	fractal_dimension_worst
0	1	17.99	10.38	122.80	1001.0	0.11840	0.27760	0.3001	0.14710	0.2419	...	25.38	17.33	184.60	2019.0	0.1622	0.6656	0.7119	0.2654	0.4601	0.11890
1	1	20.57	17.77	132.90	1326.0	0.08474	0.07864	0.0869	0.07017	0.1812	...	24.99	23.41	158.80	1956.0	0.1238	0.1866	0.2416	0.1860	0.2750	0.08902
2	1	19.69	21.25	130.00	1203.0	0.10960	0.15990	0.1974	0.12790	0.2069	...	23.57	25.53	152.50	1709.0	0.1444	0.4245	0.4504	0.2430	0.3613	0.08758
3	1	11.42	20.38	77.58	386.1	0.14250	0.28390	0.2414	0.10520	0.2597	...	14.91	26.50	98.87	567.7	0.2098	0.8663	0.6869	0.2575	0.6638	0.17300
4	1	20.29	14.34	135.10	1297.0	0.10030	0.13280	0.1980	0.10430	0.1809	...	22.54	16.67	152.20	1575.0	0.1374	0.2050	0.4000	0.1625	0.2364	0.07678

5 rows × 31 columns

Applied the numerical encoding of the target variable to the dataset.

df.isnull().values.any()

np.False_

There are no null values.

# Plot histograms for each feature
df.hist(bins=15, figsize=(20, 15), layout=(6, 6))
plt.tight_layout()
plt.show()

The dataset is slightly imbalanced. Most features seem to follow a normal distribution (perhaps with a positive skewness). For the rest it's feasible to apply a log-transform.

skewness_arr = df.skew().sort_values(ascending=False)
skewness_arr = skewness_arr[skewness_arr > 2]
print(skewness_arr)

skewness_arr = skewness_arr.index.tolist()

# Add 1 to every skewed data since log(0) is undefined and log(epsilon) is large
df[skewness_arr] = df[skewness_arr].apply(lambda x: np.log(x + 1))
df[df.columns.difference(['diagnosis'])] = preprocessing.StandardScaler().fit_transform(df[df.columns.difference(['diagnosis'])])

area_se                 5.447186
concavity_se            5.110463
fractal_dimension_se    3.923969
perimeter_se            3.443615
radius_se               3.088612
smoothness_se           2.314450
symmetry_se             2.195133
dtype: float64

Select features with a large positive skewness to apply log-transform.
After that, standardize every feature (except diagnosis) with StandardScaler().

df.hist(bins=15, figsize=(20, 15), layout=(6, 6))
plt.tight_layout()
plt.show()

# Plot the correlation matrix
plt.figure(figsize=(12, 10))
correlation_matrix = df.corr()
sns.heatmap(correlation_matrix, annot=True, fmt=".2f", cmap='coolwarm', linewidths=0.5).figure.set_size_inches(20, 10)
plt.title('Correlation Matrix')
plt.show()

The eventual diagnosis correlates well with the "size" (perimeter, radius, area) and concavity of the nucleus. Generally, the dataset seems to be highly correlated, altough there are several irrelevant correlations between features that measure roughly the same thing (mean, worst, se for every feature).

# Plot pairplot for a subset of features
sns.pairplot(
    df[["diagnosis", "radius_mean", "texture_mean", "perimeter_mean", "area_mean",
        "smoothness_mean", "compactness_mean", "concavity_mean", "concave points_mean", "symmetry_mean",
        "fractal_dimension_mean" ]],
    hue = "diagnosis",
    palette={1: 'orange', 0: 'blue'}
)
plt.show()

Overall, the data is well separated. The only features that are not well-separated are fractal_dimension, symmetry, smoothness and texture.
We can also observe that the larger the nucleus is (measured by the radius, perimeter and area) there is a higher probability of having malignant breast cancer.
Concavity shows similar properties but there are a few outliers.

Training

In general, we will use cross-validation and a Grid/Random search for hyperparameter optimalization.

Neural Network

from sklearn.neural_network import MLPClassifier
from sklearn.model_selection import train_test_split, GridSearchCV, StratifiedKFold, cross_val_score
from sklearn.metrics import classification_report

X = df.drop('diagnosis', axis=1)
y = df['diagnosis']

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

mlp = MLPClassifier(random_state=1, max_iter=10000)

param_grid = {
    'hidden_layer_sizes': [(8,), (16,), (32,), (16, 16)],
    'activation': ['tanh', 'relu'],
    'solver': ['adam', 'sgd'],
    'learning_rate_init': [0.001, 0.01, 0.1],
    'alpha': [0.0001, 0.001, 0.01],
}

stratified_kf = StratifiedKFold(n_splits=5, shuffle=True, random_state=42)

grid_search = GridSearchCV(
    estimator=mlp,
    param_grid=param_grid,
    cv=stratified_kf,
    scoring='f1',
    n_jobs=-1 
)

grid_search.fit(X_train, y_train)
best_model = grid_search.best_estimator_
y_pred = best_model.predict(X_test)
print("Classification Report:\n", classification_report(y_test, y_pred))

Classification Report:
               precision    recall  f1-score   support

           0       0.97      0.99      0.98        71
           1       0.98      0.95      0.96        43

    accuracy                           0.97       114
   macro avg       0.97      0.97      0.97       114
weighted avg       0.97      0.97      0.97       114

Logistic Regression

from sklearn.linear_model import LogisticRegression

logreg = LogisticRegression()
logreg.fit(X_train, y_train)
logreg.score(X_test, y_test)
y_pred = logreg.predict(X_test)
print("Classification Report:\n", classification_report(y_test, y_pred))

array([[ 0.42170575,  0.4597363 ,  0.38992846,  0.45428822,  0.07404599,
        -0.52730425,  0.83194298,  1.11157693, -0.24781408, -0.06299014,
         1.17960835, -0.19665484,  0.16687914,  1.06692987,  0.29099273,
        -0.68468889, -0.17897315,  0.37137957, -0.65938838, -0.63642068,
         0.74226631,  1.32019565,  0.49342255,  0.71976254,  0.51230787,
         0.03009625,  0.98072941,  0.70117948,  1.26855711,  0.19026785]])

Random Forest

from sklearn.ensemble import RandomForestClassifier

rf = RandomForestClassifier(random_state=42)

param_grid = {
    'n_estimators': [100, 200, 300],
    'max_depth': [None, 10, 20, 30],
    'min_samples_split': [2, 5, 10],
    'min_samples_leaf': [1, 2, 4],
    'bootstrap': [True, False],
}

stratified_kf = StratifiedKFold(n_splits=5, shuffle=True, random_state=42)

grid_search = GridSearchCV(
    estimator=rf,
    param_grid=param_grid,
    cv=stratified_kf,
    scoring='f1',
    n_jobs=-1
)

grid_search.fit(X_train, y_train)

best_model = grid_search.best_estimator_
y_pred = best_model.predict(X_test)
print("Classification Report:\n", classification_report(y_test, y_pred))

Classification Report:
               precision    recall  f1-score   support

           0       0.96      0.97      0.97        71
           1       0.95      0.93      0.94        43

    accuracy                           0.96       114
   macro avg       0.96      0.95      0.95       114
weighted avg       0.96      0.96      0.96       114

Further Questions

Now, we look at a few further questions worth investigating.

Which features are the most important?

cols = list(df.columns)
cols.remove('diagnosis')
for pair in sorted(zip(cols, best_model.feature_importances_), key=lambda x: x[1], reverse=True):
    # print(f"{pair[0]}: {round(pair[1], 3)}")
    pass

feature_importances = best_model.feature_importances_
feature_df = pd.DataFrame({
    'Feature': cols,
    'Importance': feature_importances
})

feature_df = feature_df.sort_values(by='Importance', ascending=False)

plt.figure(figsize=(10, 6))
sns.barplot(x='Importance', y='Feature', data=feature_df, hue='Feature', palette='viridis', legend=False)
plt.title('Feature Importances from Random Forest')
plt.xlabel('Importance')
plt.ylabel('Feature')
plt.show()

We can use the Random Forest model's .feature_importances_ property to see which features correlate the most with having malignant breast cancer.
The top features are concavity, area, radius and perimeter and this aligns well with the biological interpretation since large radius and irregular texture often indicate malignancy because malignant tumors tend to grow and invade surrounding tissue.